Gone over with a fine toothcomb

As the fine-print of David Coleman Headley's 36-page plea agreement is gone over with a fine toothcomb, the question now is whether Indian investigators will have access to the Lashkar-e-Toiba operative and if so, what kind of access.
The 36-page plea agreement specifically enlists the conditions for cooperation. It requires him to "fully and truthfully cooperate in any manner in which he is called upon to cooperate" by a representative of the United States Attorney's Office for the Northern District of Illinois. It requires him to "fully and truthfully testify in any foreign judicial proceedings held in the United States by way of deposition, videoconferencing or letters rogatory."

Could you please explain to me the emboldened parts?

I also don't know the meaning of "gone over" and "toothcomb" in this context.

Source : http://www.ndtv.com/news/india/reports-say-denmark-got-to-quiz-headley-18048.php